1.
A research team must carry 58 rock samples down the mountain. Each pack holds 8 samples, and every sample must come down. How many packs do they need, and how many samples are in the last one?
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Answer:
Did you know? Fresh lava can reach 2,100°F — hot enough to melt a copper penny in seconds.
2.
A visitor centre has 91 helmets to store on shelves of 9. How many shelves are completely full, and how many helmets are left over?
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Answer:
Did you know? Volcanologists wear silver heat suits that reflect radiant heat, which is why they look like astronauts.
3.
A museum starts with 342 volcanic rocks, sends 158 to a school, and then collects 96 more on a field trip. How many rocks does it have now?
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Answer:
Did you know? Pumice is the only rock that floats — it's full of gas bubbles frozen in place.
4.
An observation post has 7 windows and each window has 8 panes. During an eruption, 19 panes crack. How many panes are still whole?
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Answer:
Did you know? Volcanic ash isn't soft like fire ash — it's tiny shards of glass, which is why it scratches everything.
5.
A team of 46 scientists is going up in cable cars that hold 5 people each. Everyone must ride. How many cable cars are needed, and how many people are in the last car?
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Answer:
Did you know? Mount Etna in Sicily has been erupting on and off for at least 500,000 years.
1.
An ash cloud covers 3/8 of a valley on the first day and another 1/2 of the valley on the second day. What fraction of the valley is covered? What fraction is still clear?
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Answer:
Did you know? The 1815 eruption of Tambora threw up so much ash that 1816 was called 'the year without a summer' in Europe and North America.
2.
A lava flow travels 2/3 of a mile in the morning and 1/6 of a mile in the afternoon. How far did it travel that day?
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Answer:
Did you know? Most lava flows move slower than walking pace — you can usually stroll away from one.
3.
A monitoring station's battery is 7/10 charged. Overnight it uses 1/4 of a full charge. What fraction of the battery is left?
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Answer:
Did you know? Seismometers around a volcano can detect movement smaller than the width of a human hair.
4.
A crater rim trail is 4/5 of a mile long. Aisha hikes 1/3 of a mile and stops. What fraction of a mile is left to walk?
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Answer:
Did you know? Crater lakes can be more acidic than lemon juice because volcanic gases dissolve into the water.
5.
Scientists have mapped 5/6 of a lava tube. A cave-in blocks off 1/4 of the whole tube, which they can no longer reach. What fraction of the tube have they mapped and can still reach?
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Answer:
Did you know? Lava tubes form when the outside of a flow cools into a crust while molten rock keeps running through the middle.
3rd Grade (remainders)
1. 8 packs; 2 samples in the last one.
58 ÷ 8 = 7 r 2. All must come down → 8 packs, last holds 2.
2. 10 full shelves, 1 helmet left.
91 ÷ 9 = 10 r 1. Completely full only → 10 shelves, 1 helmet over.
3. 280 rocks.
342 − 158 = 184. Then 184 + 96 = 280.
4. 37 panes whole.
7 × 8 = 56 panes. 56 − 19 cracked = 37.
5. 10 cable cars; 1 person in the last.
46 ÷ 5 = 9 r 1. Everyone rides → 10 cars, last carries 1.
4th Grade (unlike denominators)
1. Covered 7/8; 1/8 still clear.
Common bottom 8. 3/8 + 4/8 = 7/8. Clear: 8/8 − 7/8 = 1/8.
2. 5/6 of a mile.
Common bottom 6. 2/3 = 4/6. 4/6 + 1/6 = 5/6.
3. 9/20 of the battery.
Common bottom 20. 7/10 = 14/20, 1/4 = 5/20. 14/20 − 5/20 = 9/20.
4. 7/15 of a mile left.
Common bottom 15. 4/5 = 12/15, 1/3 = 5/15. 12/15 − 5/15 = 7/15.
5. 7/12 of the tube.
Common bottom 12. 5/6 = 10/12, 1/4 = 3/12. 10/12 − 3/12 = 7/12.